Abstract
Relative parametric canonical wreath homology and cohomology groups of an arbitrary metrizable space over pairs of copresheaves and presheaves are defined. Duality theorems are proved for these groups. Furthermore, based on epimorphisms of pairs of presheaves (copresheaves), exact and semi-exact cohomological (homological) sequences are constructed which estimate relative parametric canonical wreath cohomology (homology) groups over the pairs of presheaves (copresheaves) by means of relative parametric canonical wreath cohomology (homology) groups.
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